Data-driven CFD scaling of bioinspired Mars flight vehicles for hover

Abstract

One way to improve our model of Mars is through aerial sampling and surveillance, which could provide information to augment the observations made by ground-based exploration and satellite imagery. Flight in the challenging ultra-low-density Martian environment can be achieved with properly scaled bioinspired flapping wing vehicle configurations that utilize the same high lift producing mechanisms that are employed by insects on Earth. Through dynamic scaling of wings and kinematics, we investigate the ability to generate solutions for a broad range of flapping wing flight vehicles with masses ranging from insects O(10⁻³) kg to the Mars helicopter Ingenuity O(10⁰) kg. A scaling method based on a neural-network trained on 3D Navier-Stokes solutions is proposed to determine approximate wing size and kinematic values that generate bioinspired hover solutions. We demonstrate that a family of solutions exists for designs that range from 1 to 1000 g, which are verified and examined using a 3D Navier-Stokes solver. Our results reveal that unsteady lift enhancement mechanisms, such as delayed stall and rotational lift, are present in the bioinspired solutions for the scaled vehicles hovering in Martian conditions. These hovering vehicles exhibit payloads of up to 1 kg and flight times on the order of 100 min when considering the respective limiting cases of the vehicle mass being comprised entirely of payload or entirely of a battery and neglecting any transmission inefficiencies. This method can help to develop a range of Martian flying vehicle designs with mission viable payloads, range, and endurance.

Introduction

Improved information about the Martian environment will reduce uncertainties and risks in future exploration, including human missions. Aerial vehicles can perform sensing and other tasks that fill the gaps in the information gathering capabilities of Mars orbiters and land-based rovers. Flight vehicles capable of near-surface hovering are attractive candidates for such information gathering missions. These missions may include surveying remote locations, retrieving samples, efficiently generating topographic models of the surrounding terrain, providing near-surface weather data, and assisting rovers in path planning. In addition, the recent advancements in swarming flight and autonomy offer additional design options and possibly improved efficiencies for these missions [1].

Though the atmospheric viscosity on Mars is similar to that of Earth, μ_Mars = 0.83μ_Earth [2], the ultra-low density atmospheric environment has proved a difficult challenge in designing realizable Martian flight vehicles. Despite the gravitational acceleration on Mars requiring less lift production than on Earth for a given vehicle mass, where g_Mars = 0.38g_Earth, the reduced density on Mars compared to Earth being ρ_Mars = 0.0142ρ_Earth can be quite prohibitive for generating sufficient aerodynamic forces to fly using conventional designs [3]. Although NASA is sending the helicopter Ingenuity to Mars during the 2020 Perseverance rover mission, such a solution results in a design that is relatively large (around 1.8 kg vehicle with a 1.21 m rotor diameter) [4] and potentially less aerodynamically efficient when operated at the low Reynolds numbers inherent to Martian flight [5].

Bioinspired flapping wing solutions can overcome the difficulties associated with flight in the rarefied Martian atmosphere [6]. The thin Martian atmosphere results in a relatively low Reynolds number Re which is directly proportional to the fluid density ρ. Insects make use of efficient, unsteady aerodynamic mechanisms that occur at low Reynolds numbers. These mechanisms include delayed stall via an attached leading-edge vortex (LEV), wake capture, and enhanced circulation via rotational lift [7,8]. As such, properly scaled flapping wing motion on Mars has been demonstrated to exhibit the same mechanisms and potential for flight [6,9].

The method used to achieve these bioinspired solutions on Mars is based on the well-established fluid dynamics concept of dynamic similarity [10,11]. In general, to dynamically scale a system in the context of fluid dynamics is to preserve the geometrical shape but change the relevant dimensional parameters (e.g. fluid density, viscosity, wing velocity, etc.) such that the set of governing dimensionless parameters (e.g. Reynolds number, lift coefficient, etc.) is preserved between the two configurations. For example, dynamic similarity guides the scaling of model aircraft for sub-scale wind tunnel tests before full-scale flight tests are performed. Not only does dynamic similarity allow for convenient physical scaling of the system, it also reduces the total number of parameters required to fully describe a system involving multiple parameters, thus reducing the design space to a more manageable set of parameters [12].

Our previous bioinspired solutions [6] are dynamically similar to terrestrial insects' flapping wing motions, and take advantage of similar unsteady, high lift coefficient producing mechanisms on Mars. The relevant set of dimensionless parameters for a rigid flapping wing are: aspect ratio AR, related to the slenderness of a wing; Reynolds number Re, the ratio between the flow inertia and viscous forces; reduced frequency k, a measure of flow unsteadiness; Mach number M, related to the flow compressibility; and pitch amplitude A, measuring the wing's angle of attack. To maintain dynamic similarity with insects on Earth, these parameters were kept in the insect-inspired flight regime. Starting from the morphological parameters corresponding to a bumblebee, the wings were uniformly scaled to approximately the size of cicada wings. The flapping frequency was also reduced to 63 Hz, approximately 43% that of a bumblebee (~155 Hz). Generating such a solution through biomimicry not only provides a means of producing sufficient lift, but it also results in a flight vehicle that has the potential to benefit from other attractive qualities of insect flight such as hovering, high maneuverability, long range/endurance flight, and high payload capacity. To exploit the advantages of insect-inspired flight, we extended the study to quantify the payload margin of the bumblebee-inspired flapping wing micro air vehicle (FWMAV) and determined that it can carry a payload on the order of its own body weight [13]. It was determined that the payload capabilities are limited by maintaining dynamically similar motion.

While successful flapping wing flight on Mars has been simulated [6,9], these results were limited to vehicle masses that were less than 1 g, operated at Reynolds numbers of less than 200, and reduced frequencies between 0.2 and 0.35. The general scaling range between viable insect-inspired flapping wing vehicles and infeasible designs is currently unknown.

This paper seeks to identify the physical solution range for bioinspired flapping wing flight on Mars. We present a data-driven CFD scaling model that accounts for nonlinearities in the mean lift based on the relevant dimensionless parameters. Using this method, we generate hover solutions for flapping wing vehicles on Mars that range from 1 g to 1 kg. We verify these bioinspired solutions using a well-validated 3D Navier-Stokes equation solver. Furthermore, we investigate the resulting dimensional design space to understand the trends and limits of scaling a bioinspired flapping wing vehicle for flight on Mars. Our previous solution at the insect scale [13] had a mass of 0.2 g. Current Earth-based flapping wing robots have masses of O(10⁰–10¹) grams. These include Chiba University's bioinspired MAV (6 g) [14], the DelFly II (16 g) [15], the Nano Hummingbird (19 g) [16], the KUBeetle-S (16 g) [17,18], and various other FWMAV prototypes (6 and 12 g) [19]. Additionally, the Mars helicopter Ingenuity mass is O(10³) grams [4]. While insect size micro-air vehicles can employ stealth, larger vehicles with increased payload capability can be more beneficial for Mars exploration since they can carry larger sensors than insect-size vehicles. We provide a method for generating dynamically similar hovering design solutions for Martian flapping wing robots with total masses on the order of the current Earth FWMAVs, as well as the Mars helicopter Ingenuity.